

A136412


a(n) = (5*4^n+1)/3.


7



2, 7, 27, 107, 427, 1707, 6827, 27307, 109227, 436907, 1747627, 6990507, 27962027, 111848107, 447392427, 1789569707, 7158278827, 28633115307, 114532461227, 458129844907, 1832519379627, 7330077518507, 29320310074027
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OFFSET

0,1


COMMENTS

An Engel expansion of 4/5 to the base b := 4/3 as defined in A181565, with the associated series expansion 4/5 = b/2 + b^2/(2*7) + b^3/(2*7*27) + b^4/(2*7*27*107) + .... Cf. A199115 and A140660.  Peter Bala, Oct 29 2013


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,4).


FORMULA

a(n) = 4*a(n1)1.
O.g.f.: (2+3*x)/((1+x)*(1+4*x)).  R. J. Mathar, Apr 04 2008
a(n) = 5*a(n1)4*a(n2).  Vincenzo Librandi, Nov 04 2011


PROG

(MAGMA) [(5*4^n+1)/3: n in [0..30]]; // Vincenzo Librandi, Nob 04 2011
(Haskell)
a136412 = (`div` 3) . (+ 1) . (* 5) . (4 ^)
 Reinhard Zumkeller, Jun 17 2012
(PARI) a(n)=(5*4^n+1)/3 \\ Charles R Greathouse IV, Oct 07 2015


CROSSREFS

Cf. A007583. Cf. A007302. A140660, A181565, 1/3 of A199115.
Sequence in context: A150592 A150593 A024429 * A192417 A150594 A150595
Adjacent sequences: A136409 A136410 A136411 * A136413 A136414 A136415


KEYWORD

nonn,easy


AUTHOR

Paul Curtz, Mar 31 2008


EXTENSIONS

Formula in definition and more terms from R. J. Mathar, Apr 04 2008


STATUS

approved



